We observe two metal-poor main sequence stars that are members of the recently-discovered Sylgr stellar stream. We present radial velocities, stellar parameters, and abundances for 13 elements derived from high-resolution optical spectra collected using the Magellan Inamori Kyocera Echelle spectrograph. The two stars have identical compositions (within 0.13 dex or 1.2 sigma) among all elements detected. Both stars are very metal poor ([Fe/H] = -2.92 +/- 0.06). Neither star is highly enhanced in C ([C/Fe] < +1.0). Both stars are enhanced in the alpha elements Mg, Si, and Ca ([alpha/Fe] = +0.32 +/- 0.06), and ratios among Na, Al, and all Fe-group elements are typical for other stars in the halo and ultra-faint and dwarf spheroidal galaxies at this metallicity. Sr is mildly enhanced ([Sr/Fe] = +0.22 +/- 0.11), but Ba is not enhanced ([Ba/Fe] < -0.4), indicating that these stars do not contain high levels of neutron-capture elements. The Li abundances match those found in metal-poor unevolved field stars and globular clusters (log epsilon (Li) = 2.05 +/- 0.07), which implies that environment is not a dominant factor in determining the Li content of metal-poor stars. The chemical compositions of these two stars cannot distinguish whether the progenitor of the Sylgr stream was a dwarf galaxy or a globular cluster. If the progenitor was a dwarf galaxy, the stream may originate from a dense region such as a nuclear star cluster. If the progenitor was a globular cluster, it would be the most metal-poor globular cluster known.
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